結果

問題 No.1078 I love Matrix Construction
ユーザー stoq
提出日時 2020-12-04 19:18:31
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 67 ms / 2,000 ms
コード長 6,831 bytes
コンパイル時間 3,235 ms
コンパイル使用メモリ 218,964 KB
最終ジャッジ日時 2025-01-16 15:59:47
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
other AC * 22
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ソースコード

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#define MOD_TYPE 1
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
#if 0
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif
#if 1
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;
constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
constexpr double PI = acos(-1.0);
constexpr double EPS = 1e-7;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};
#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";
struct io_init
{
  io_init()
  {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(30) << setiosflags(ios::fixed);
  };
} io_init;
template <typename T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b)
{
  return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
  fill((T *)array, (T *)(array + N), val);
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept
{
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> &p) noexcept
{
  os << p.first << " " << p.second;
  return os;
}
#pragma endregion
namespace atcoder
{
  namespace internal
  {
    template <class E>
    struct csr
    {
      std::vector<int> start;
      std::vector<E> elist;
      csr(int n, const std::vector<std::pair<int, E>> &edges)
          : start(n + 1), elist(edges.size())
      {
        for (auto e : edges)
        {
          start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++)
        {
          start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges)
        {
          elist[counter[e.first]++] = e.second;
        }
      }
    };
    // Reference:
    // R. Tarjan,
    // Depth-First Search and Linear Graph Algorithms
    struct scc_graph
    {
    public:
      scc_graph(int n) : _n(n) {}
      int num_vertices() { return _n; }
      void add_edge(int from, int to) { edges.push_back({from, {to}}); }
      // @return pair of (# of scc, scc id)
      std::pair<int, std::vector<int>> scc_ids()
      {
        auto g = csr<edge>(_n, edges);
        int now_ord = 0, group_num = 0;
        std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
        visited.reserve(_n);
        auto dfs = [&](auto self, int v) -> void {
          low[v] = ord[v] = now_ord++;
          visited.push_back(v);
          for (int i = g.start[v]; i < g.start[v + 1]; i++)
          {
            auto to = g.elist[i].to;
            if (ord[to] == -1)
            {
              self(self, to);
              low[v] = std::min(low[v], low[to]);
            }
            else
            {
              low[v] = std::min(low[v], ord[to]);
            }
          }
          if (low[v] == ord[v])
          {
            while (true)
            {
              int u = visited.back();
              visited.pop_back();
              ord[u] = _n;
              ids[u] = group_num;
              if (u == v)
                break;
            }
            group_num++;
          }
        };
        for (int i = 0; i < _n; i++)
        {
          if (ord[i] == -1)
            dfs(dfs, i);
        }
        for (auto &x : ids)
        {
          x = group_num - 1 - x;
        }
        return {group_num, ids};
      }
      std::vector<std::vector<int>> scc()
      {
        auto ids = scc_ids();
        int group_num = ids.first;
        std::vector<int> counts(group_num);
        for (auto x : ids.second)
          counts[x]++;
        std::vector<std::vector<int>> groups(ids.first);
        for (int i = 0; i < group_num; i++)
        {
          groups[i].reserve(counts[i]);
        }
        for (int i = 0; i < _n; i++)
        {
          groups[ids.second[i]].push_back(i);
        }
        return groups;
      }
    private:
      int _n;
      struct edge
      {
        int to;
      };
      std::vector<std::pair<int, edge>> edges;
    };
  } // namespace internal
} // namespace atcoder
namespace atcoder
{
  // Reference:
  // B. Aspvall, M. Plass, and R. Tarjan,
  // A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean
  // Formulas
  struct two_sat
  {
  public:
    two_sat() : _n(0), scc(0) {}
    two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
    void add_clause(int i, bool f, int j, bool g)
    {
      assert(0 <= i && i < _n);
      assert(0 <= j && j < _n);
      scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
      scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
    }
    bool satisfiable()
    {
      auto id = scc.scc_ids().second;
      for (int i = 0; i < _n; i++)
      {
        if (id[2 * i] == id[2 * i + 1])
          return false;
        _answer[i] = id[2 * i] < id[2 * i + 1];
      }
      return true;
    }
    std::vector<bool> answer() { return _answer; }
  private:
    int _n;
    std::vector<bool> _answer;
    internal::scc_graph scc;
  };
} // namespace atcoder
void solve()
{
  int n;
  cin >> n;
  vector<int> s(n), t(n), u(n);
  rep(i, n) cin >> s[i], s[i]--;
  rep(i, n) cin >> t[i], t[i]--;
  rep(i, n) cin >> u[i];
  atcoder::two_sat ts(n * n);
  rep(i, n)
  {
    bool a = !(u[i] & 1), b = !(u[i] & 2);
    rep(j, n)
    {
      int p = s[i] * n + j, q = j * n + t[i];
      ts.add_clause(p, a, q, b);
    }
  }
  bool ex = ts.satisfiable();
  if (!ex)
  {
    cout << -1 << "\n";
    return;
  }
  auto ans = ts.answer();
  rep(i, n * n)
  {
    cout << ans[i] << (i % n == n - 1 ? "\n" : " ");
  }
}
int main()
{
  solve();
}
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